The time-of-flight (TOF) method of mass spectrometry is based on a measurement of the time it takes for ions to fly from an ion source to a detector along the same path. The ion source simultaneously produces pulses of ions having different mass-to-charge ratios but of the same average energy. Thus, due to the laws of motion in an electrostatic field the flight time for ions having different mass-to-charge ratios (m/e) is inversely proportional to the square root of m/e. Ions arriving at the detector produce pulses of current which are measured by a control system and presented in the form of a spectrum. The mass-to-charge ratio of ions under investigation can be derived by comparing the position of their peak with respect to peaks of known ions (relative calibration) or by direct measurement of arrival time (absolute calibration). The narrower the peak of ions of similar mass the higher the accuracy of mass measurement provided that voltage supply and system dimensions are stable. For various types of mass-spectrometer relative peak width is characterised by a resolving power—the ratio of apparent mass to the peak width in mass units: Rm=m/Δm. In the case of TOF mass spectrometers the mass resolving power is equal to one half of a ratio of the total flight time with respect to the peak width in time units: Rm=0.5 t/Δt. Thus, in order to achieve higher accuracy, it is necessary_either to reduce peak width as much as possible or to increase the flight time.
There are certain limitations to reducing peak width in TOF mass spectrometers. Even for ions having the same mass-to-charge ratio the ion source produces particles of similar, but slightly different energy. This is due to an initial spatial spread of ions in the ion source prior their to ejection. It is essential to optimise electrostatic fields in a TOF mass spectrometer in such way that ions having the same mass-to-charge ratio but different energies arrive at the detector at the same time. Thus, an ion optical path in TOF mass spectrometers is “energy isochronous” along the flight path direction. By appropriate optimisation, a high level of isochronicity can be achieved so that ions arrive at the detector at times that have very little dependence on their initial positions inside the ion source. Further reduction of the peak width is limited by the initial velocity spread of ions. The latter results in so-called “turn-around time” which is the difference of arrival times of ions having an initial velocity vT in a direction along the flight path and an initial velocity −vT in an opposite direction along the flight path. The difference is inversely proportional to a strength of electrical field at the moment of ion extraction from the ion source: tturn=2 vT/(eE/m). One way to reduce turn around time is to reduce the initial velocity vT, for example by cooling ions inside the source, another way is to increase the field strength. Both approaches have certain practical limitations, which are almost exhausted in modem TOF mass spectrometry.
Another way to improve mass resolving power is to increase the flight time using a longer flight path. Although it is possible to increase the flight path simply by increasing the size of the instrument, this method is impractical because modern TOF systems already have a typical size of 1 m. An elegant way to increase the flight path is to use multiple reflections at electrostatic mirrors. Some known multiply-reflecting systems attempt to satisfy several conditions at the same time; that is, a multiply-folded beam trajectory along which the flight time of ions having the same mass-to-charge ratio, but different energies, is substantially independent of energy within an energy range produced by the ion source (longitudinal isochronicity), stable ion motion in the transverse direction so that the ion beam can survive multiple reflections, and a time-of-flight that is substantially independent of angular and spatial spread of the ion beam in the lateral direction (minimum lateral aberrations). These conditions have proved to be difficult to satisfy simultaneously, and know systems that do satisfy the conditions tend to be difficult to manufacture and/or lack flexibility.